Twisted or oscillated plywood structure can be often found in biological composites such as claws of lobsters, bone of mammals, dactyl club of mantis shrimps, and exoskeleton of beetles, which exhibits a combination of high stiffness, high fracture toughness and low density. However, there lacks a quantitative understanding of the relationship between the fracture toughness of the composite and its internal geometry. In this article, we propose that a combination of crack tilting and crack bridging determines the effective fracture toughness of the fiber-reinforced composite with the plywood structure. During the fracturing process, a crack plane initially propagates in the matrix-fiber interface following the twisted fiber alignment. Such crack tilting mechanism can significantly enlarge the area of cracking surface and thus enhance the effective fracture toughness of the composite. With the propagation of the tilted crack plane, the local energy release rate becomes too small to maintain the growth of the tilted crack plane, leading the crack to grow into the matrix, crossing the fibers. Because of the high strength of the fiber, a few fibers can maintain unbroken behind the crack tip, corresponding to crack bridging mechanism. Based on our quantitative analysis, it is found that the effective fracture toughness of the composite can be maximized for a certain pitch angle of the oscillated/twisted plywood structure, which agrees well with experiments. STATEMENTS OF SIGNIFICANCE: Fiber-reinforced composites can be widely found in nature and engineering applications. Recently, it has been discovered that many fiber-reinforced composites in biology have twisted or oscillated plywood structure with high fracture toughness, high mechanical stiffness and low density. Detailed experiments have indicated that an optimal pitch angle may exist for the plywood structure to maximize the fracture toughness of the composites. However, there lacks a quantitative model of revealing such pitch angle-dependent fracture toughness. In this work, we propose a hybrid toughening mechanism and predict the optimal pitch angle in twisted/oscillated plywood structure for maximizing the fracture toughness. Our predictions agree reasonably well with experimental results. As such, the theory may help the design of better fiber-reinforced composites.Copyright © 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.